I agree that I really do not want to jump in and get my feet wet on
something like this. My problem is I'm not sure if my family's budget
can take a big bill by calling in a electrician. I realize that this
is something that I cannot cut corners on and more than anything safety
for my family is the most important thing.

With that said I have done some minor things like replacing some
switches, wall outlets, light fixtures, and ceiling fans. However, I
have never done anything with the wiring (aside from using existing
wiring) or the breaker panel.

Another person replied prior and suggested using an inexpensive tester
to test the outlet. Are these testers reliable? If I use one and
determine that the outlet is truly wired in reverse polarity, if I
were to fix (probably replace) that outlet and ensure that it is wired
correctly can I consider this issue resolved or could there potentially
be other problems that this kind of tester would not show?

Also, John mentions "Using a voltmeter I would check each side of the
receptacle to ground and to each other." I have had some experience
with a voltmeter, but when I check each side to the ground versu
checking to each other, what results should I expect?

Again, I by all means do not want to cut corners and only "patch" this
problem and still have other existing problems, but if this could take
care of this issue until I can financially work out having a big
expense associated with having a professional come in would be
preferred.

Thank you to everyone who has responded, it is greatly appreciated.